Doğrusal olmayan üretim maliyeti fonksiyonları olan kafile büyüklüğü problemi

We study different variations of the lot sizing problem encountered in many real life production, procurement and transportation systems. First, we consider the deterministic lot sizing problem with piecewise concave production cost functions. We develop a dynamic programming (DP) algorithm to solve the problem and show that the problem is polynomially solvable when number of breakpoints of the production cost function is fixed and the breakpoints are time-invariant. We observe that the time complexity of our algorithm is as good as the complexity of existing algorithms developed for some special cases. Our algorithm performs quite well for small and medium sized instances. For larger instances, we propose a DP based heuristic. Next, we consider the stochastic lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function. We formulate the problem as a second-order cone mixed integer program, strengthen the formulation and solve it by a commercial solver. Moreover, we obtain some convex hull and computational complexity results. As a final problem, we study the multistage stochastic lot sizing problem with nervousness considerations and controllable processing times. System nervousness is one of the main problems of dynamic solution strategies developed for stochastic lot sizing problems. We formulate the problem so that the nervousness of the system is restricted. We develop valid inequalities for the problem based on some mixing set relaxations of our formulation and computationally test these inequalities.